...recall the concept of "dimension" for metric spaces and some of its properties. A metric space (A/, d) is said to be separable if there exists a countable subset S of M such that S = M. 1.2. DEFINITION, (i) The void set and only it is of dimension — I. (ii) If...

...dense in a metric space (X, d), if E = X, or, equivalently, Vx € X 3xn e E such that xn — > x The space (X, d} is said to be separable if there exists a countable set E dense in X. Topological Equivalence. Two metric spaces X = (X, d) and Y = (Y, p) are topologically...

...sequence — ie, whenever for each e > 0 there exists N£ such that d(xm, xn) < £ for all m, n > N. A metric space (X, d) is said to be separable if there is a countable set {xn \ n = 1,2,...} m X whose closure is the whole of X . A Polish space is defined...